| Date | May Specimen | Marks available | 2 | Reference code | SPM.1.sl.TZ0.13 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 13 | Adapted from | N/A |
Question
A liquid is heated so that after \(20\) seconds of heating its temperature, \(T\) , is \({25^ \circ }{\text{C}}\) and after \(50\) seconds of heating its temperature is \({37^ \circ }{\text{C}}\) .
The temperature of the liquid at time \(t\) can be modelled by \(T = at + b\) , where \(t\) is the time in seconds after the start of heating.
Using this model one equation that can be formed is \(20a + b = 25\) .
Using the model, write down a second equation in \(a\) and \(b\) .
Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .
Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of heating.
Markscheme
\(50a + b = 37\) (A1)(A1) (C2)
Note: Award (A1) for \(50a + b\) , (A1) for \(= 37\) .
\(a = 0.4\), \(b = 17\) (A1)(ft)(A1)(ft) (C2)
Notes: Award (M1) for attempt to solve their equations if this is done analytically. If the GDC is used, award (ft) even if no working seen.
\(T = 0.4(60) + 17\) (M1)
Note: Award (M1) for correct substitution of their values and \(60\) into equation for \(T\).
\(T = 41{\text{ }}{{\text{(}}^ \circ }{\text{C}})\) (A1)(ft) (C2)
Note: Follow through from their part (b).
